hard to tell but it looks like some repointing has happened in cement mortar, this will trap water in and force it through the inside. very common with 9" solid walls which yours almost certainly is from that period. Check its all lime for starters.
May have a slate dpc but unlikely, our 1899 has nothing including no footing.
Brickwork should resist being soaked and dry out, if water cannot escape through the front due to modern cement it will go through to the inside.